Question

a) Assume the firm operates in the monopoly market in the long run with the demand...

a) Assume the firm operates in the monopoly market in the long run with the demand function P = 100-Q and TC = 640 + 20Q with TC showing the total cost of production, Q and P respectively of output quantity and price. Using the information above, publish
i) Total revenue function (TR)
ii) Marginal revenue (MR)
iii) Marginal cost function (MC)
iv) Determine the level of price and quantity of production that maximizes profit
v) Determine the amount of profit earned by the monopolist

1) Total revenue function = P*Q = (100-Q ) *Q = 100Q - (Q)^2

2) Marginal revenue can be found out by differentiating total revenue function with respect to Q

MR = 100 - 2Q

3) Marginal cost can be found out by differentiating total cost function with respect to Q

MC = 20

4) In order to maximize profits, the monopolist equates MR = MC

100 - 2Q = 20

Q = 80/2 = 40 units

5) Profit = total revenue - total costs = 100Q - (Q)^2 - 640 - 20Q = 4,000 - 1600 - 640 - 800 = \$960

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